Anonymization techniques have tranquilized current social network users in terms of privacy leakage, however, it does not radically prevent adversaries from de-anonymizing users, as they may map the users to an un-anonymized network. Till now, researchers share a common thread in such de-anonymization attack: unveiling conditions leading to successful de-anonymization under the chosen network model. However, it has not yet been well understand how the structural property in different network models intrinsically determines de-anonymizability. We address the above issue in this paper by making the two contributions: (i) We discover that the automorphic degree and homomorphic degree of social networks determine their de-anonymizability universally. The automorphic degree characterizes the distinguishability of the users in a network, while the homomorphic degree models the similarities of users between two networks. We conclude that a smaller automorphic degree and a larger homomorphic degree conduce to a higher de-anonymizability. Such model-independent phenomenon refreshes us with a latitudinal study as it generalizes the essential commonness of de-anonymization in different network models. (ii) We derive explicit parametric bounds of the de-anonymizability for three classic network models, showing that such bounds correspond well to our conclusion about morphism property. We then algorithmically and experimentally show that such theoretical results literally make sense to adversaries. Such longitudinal study, including welding theory, algorithm and validation, promises applicability of our results on morphism property in real cases.